Objects stuck in solid mode?
Extending lemon's commented.

An object can be restricted to a lower display mode.

In 2.79 it is set in the Properties Panel in the Object tab under the 
Display section.




  The Maximum shading mode to display in the 3D View. This can be useful if you have a high-poly object that is slowing down performance.


In 2.8 the term is Display As.